We derive the general structure of dimension-six derivative interactions in the $N$ Higgs doublet models, where Higgs fields arise as pseudo Nambu-Goldstone modes of a strongly interacting sector. We show that there are several relations among the dimension-six operators, and therefore the number of independent operators decreases compared with models on which only $SU(2{)}_L\times U(1{)}_Y$ invariance is imposed. As an explicit example, we derive scattering amplitudes and cross sections of longitudinal gauge bosons and Higgs bosons at high energy on models involving two Higgs doublets, and compare them with those of one Higgs doublet.

• Received 9 November 2011

DOI:https://doi.org/10.1103/PhysRevD.85.075021